已知x等于根号二减一，求代数式x减2/2x除以括号二加x减二减x分之四的值

Question

如题所述

Answer 1

x=√2-1
x²=2-2√2+1=3-2√2
x减2/2x除以括号二加x减二减x分之四
=x-2/2x÷(2+x-2-4/x)
=x-x÷(x-4/x)
=x-x÷[(x²-4)/x]
=x-x[x/(x²-4)]
=x-x²/(x²-4)
=√2-1-(3-2√2)/[(3-2√2)-4]
=√2-1-(3-2√2)/[3-2√2-4]
=√2-1-(3-2√2)/[-2√2-1]
=√2-1+(3-2√2)/[2√2+1]
=√2-1+(3-2√2)(2√2-1)/[(2√2+1)(2√2-1)]
=√2-1+(6√2-8-3+2√2)/[8-1]
=√2-1+(8√2-11)/7
=(7√2-7+8√2-11)/7
=(15√2-18)/7